Answered: Years Sales 1 80 3 97 4 92 4 102 6 103…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Years	Sales
1	80
3	97
4	92
4	102
6	103
8	111
10	119
10	123
11	117
13	136

You may need to use the appropriate appendix table or technology to answer this question.

The data on y = annual sales ($1,000s) for new customer accounts and x = number of years of experience for a sample of 10 salespersons provided the estimated regression equation

ŷ = 80 + 4x.

For these data,

x = 7,

Σ(x_i − x)² = 142,

and

s = 4.6098.

(a)

Develop a 95% confidence interval for the mean annual sales (in thousands of dollars) for all salespersons with nine years of experience. (Round your answers to two decimal places.)

$ thousand to $ thousand

(b)

The company is considering hiring Tom Smart, a salesperson with nine years of experience. Develop a 95% prediction interval of annual sales (in thousands of dollars) for Tom Smart. (Round your answers to two decimal places.)

$ thousand to $ thousand

(c)

Discuss the differences in your answers to parts (a) and (b).

The prediction interval is wider than the confidence interval, because you use a different critical value when developing a prediction of the annual sales for one new salesperson with nine years of experience than when developing an estimate of the mean annual sales for all salespersons with nine years of experience.

The confidence interval is wider than the prediction interval, because there is less variability associated with predicting annual sales for one new salesperson with nine years of experience than there is with estimating the mean annual sales for all salespersons with nine years of experience.

The confidence interval is wider than the prediction interval, because you use a different critical value when developing a prediction of the annual sales for one new salesperson with nine years of experience than when developing an estimate of the mean annual sales for all salespersons with nine years of experience.

The prediction interval is wider than the confidence interval, because there is more variability associated with predicting annual sales for one new salesperson with nine years of experience than there is with estimating the mean annual sales for all salespersons with nine years of experience.

The prediction interval is wider than the confidence interval, because confidence intervals are used to predict values of y for new observations corresponding to given values of x, and prediction intervals give an estimate of the mean value of y for a given value of x.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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